The 330e’s hybrid powertrain takes a bit of getting used to. The car has a multifaceted character that will seem overly complicated to those who like a car that’s simple to use; and if you’re not inclined to engage with the complication at least a little bit, you simply won’t experience this car at its best. But those who are prepared to explore the several dimensions of this car’s persona will find that it can be really convincing in so many different ways.

The column of little buttons adjacent to the gear selector, which in any other 3 Series would let you flick between Comfort, Sport and Eco-pro driving modes, are labelled differently here. There’s a Sport button among them, but otherwise there’s a host of new options.

Adaptive drive mode uses navigation route data to switch to electric mode automatically. Battery control mode allows you to restore charge

The car defaults to Hybrid mode, in which it will run electrically where it can until its drive battery is depleted before switching to run on a mix of combustion and electric power. Use Electric mode instead and a little more grunt is made available from the AC motor. It’s enough to deal with urban motoring on busy streets with a little performance to spare, although it begins to feel a bit meagre above 50mph.

Choose Sport mode or, better still, XtraBoost mode (which is the only one in which all 289bhp of power is available before you hit the accelerator pedal’s kickdown switch) and the 330e takes on an altogether more sporting flavour. It is not just hot hatch fast in outright terms but is also really responsive to part-throttle.

That sense of ever-ready responsiveness is clearest if you use the gearbox’s manual mode and ease the burden of that transmission to decide for itself whether to stick with its selected ratio or pause and downshift. The gearbox generally does a better job of quickly picking and then sticking with ratios than many plug-in hybrid (PHEV) transmissions we’ve tested, but if you really want to engage with the 330e, there’s no better way than picking gears for yourself.

At its most sporting, this car has overtaking torque to spare and revs fairly keenly beyond 5000rpm; not with the sweetness of an old BMW straight six, but with plenty of urgency and range. Brake pedal progression and feel, meanwhile – still where so many hybrids fall down – are generally good.

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